Warren_Katzenstein_PhD_Thesis_2010 pdf

Wind Power Variability, Its Cost, and Effect on Power
Plant Emissions
A Dissertation
Submitted in partial fulfillment of the requirements for the
degree of
Doctor of Philosophy
Warren Katzenstein
July 2010
Advisor
Jay Apt
Thesis Committee:
Jay Apt
Lester B. Lave
M. Granger Morgan
Gregory Reed
Allen Robinson
Carnegie Mellon University
Department of Engineering and Public Policy
Pittsburgh, Pennsylvania 15213 USA

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Copyright © 2010 by Warren Patrick Katzenstein. All rights reserved.

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Abstract
The recent growth in wind power is transforming the operation of electricity systems by
introducing variability into utilities’ generator assets. System operators are not experienced in
utilizing significant sources of variable power to meet their loads and have struggled at times to
keep their systems stable. As a result, system operators are learning in real-time how to
incorporate wind power and its variability. This thesis is meant to help system operators have a
better understanding of wind power variability and its implications for their electricity system.
Characterizing Wind Power Variability
We present the first frequency-dependent analyses of the geographic smoothing of
wind power's variability, analyzing the interconnected measured output of 20 wind plants in
Texas. Reductions in variability occur at frequencies corresponding to times shorter than ~24
hours and are quantified by measuring the departure from a Kolmogorov spectrum. At a
frequency of 2.8x10-4
Hz (corresponding to 1 hour), an 87% reduction of the variability of a
single wind plant is obtained by interconnecting 4 wind plants. Interconnecting the remaining 16
wind plants produces only an additional 8% reduction. We use step-change analyses and
correlation coefficients to compare our results with previous studies, finding that wind power
ramps up faster than it ramps down for each of the step change intervals analyzed and that
correlation between the power output of wind plants 200 km away is half that of co-located
wind plants. To examine variability at very low frequencies, we estimate yearly wind energy
production in the Great Plains region of the United States from automated wind observations at
airports covering 36 years. The estimated wind power has significant inter-annual variability and
the severity of wind drought years is estimated to be about half that observed nationally for
hydroelectric power.

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Estimating the Cost of Wind Power Variability
We develop a metric to quantify the sub-hourly variability cost of individual wind plants
and show its use in valuing reductions in wind power variability. Our method partitions wind
energy into hourly and sub-hourly components and uses corresponding market prices to
determine the cost of variability. The metric is applicable to variability at all time scales faster
than hourly, and can be applied to long-period forecast errors. We use publically available data
at 15 minute time resolution to apply the method to ERCOT, the largest wind power production
region in the United States. The range of variability costs arising from 15 minute to 1 hour
variations (termed load following) for 20 wind plants in ERCOT was $6.79 to 11.5 per MWh
(mean of $8.73 ±$1.26 per MWh) in 2008 and $3.16 to 5.12 per MWh (mean of $3.90 ±$0.52 per
MWh) in 2009. Load following variability costs decrease as wind plant capacity factors increase,
indicating wind plants sited in locations with good wind resources cost a system less to
integrate. Twenty interconnected wind plants have a variability cost of $4.35 per MWh in 2008.
The marginal benefit of interconnecting another wind plant diminishes rapidly: it is less than
$3.43 per MWh for systems with 2 wind plants already interconnected, less than $0.7 per MWh
for 4-7 wind plants, and less than $0.2 per MWh for 8 or more wind plants. This method can be
used to value the installation of storage and other techniques to mitigate wind variability.
Estimating How Wind Power Variability Affects Power Plant Emissions
Renewables portfolio standards (RPS) encourage large scale deployment of wind and
solar electric power, whose power output varies rapidly even when several sites are added
together. In many locations, natural gas generators are the lowest cost resource available to
compensate for this variability, and must ramp up and down quickly to keep the grid stable,
affecting their emissions of NOx and CO2. We model a wind or solar photovoltaic plus gas system
using measured 1-minute time resolved emissions and heat rate data from two types of natural

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gas generators, and power data from four wind plants and one solar plant. Over a wide range of
renewable penetration, we find CO2 emissions achieve ~80% of the emissions reductions
expected if the power fluctuations caused no additional emissions. Pairing multiple turbines
with a wind plant achieves ~77 to 95% of the emissions reductions expected. Using steam
injection, gas generators achieve only 30-50% of expected NOx emissions reductions, and with
dry control NOx emissions increase substantially. We quantify the interaction between state
RPSs and constraints such as the NOx Clean Air Interstate Rule (CAIR), finding that states with
substantial RPSs could see upward pressure on CAIR NOx permit prices, if the gas turbines we
modeled are representative of the plants used to mitigate wind and solar power variability.

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Acknowledgements
I would like to thank the Alfred P. Sloan Foundation, the Electric Power Research
Institute, the US National Science Foundation (under NSF Cooperative Agreement No. SES-
0345798), the Doris Duke Charitable Foundation, the Department of Energy National Energy
Technology Laboratory, the Heinz Endowments, the Pennsylvania Technology Assistance
Alliance, and the RenewElec program and Electricity Industry Center at Carnegie Mellon
University for supporting this work.
I could not have accomplished the research contained within this thesis without the
guidance and support of my advisor Jay Apt or my thesis committee of Lester Lave, Granger
Morgan, Gregory Reed, and Allen Robinson.
I would also like to thank Brett Bissinger, Jack Ellis, Emily Fertig, Elisabeth Gilmore, Lee
Gresham, Eric Hittinger, Lester B. Lave, Ralph Masiello, Hannes Pfeifenberger, Steve Rose,
Mitchell Small, Kathleen Spees, Samuel Tanenbaum, Rahul Walawalkar for their helpful
discussions and guidance. I am grateful to Tom Hansen of Tucson Electric Power for supplying
the solar PV data, the Electricity Reliability Council of Texas (ERCOT) for their publicly available
wind data, and the companies that supplied the wind and gas generator data, who wish to
remain anonymous. I would also like to express my gratitude for the help and support Patti
Steranchak, Patty Porter, Victoria Finney, Barbara Bugosh, and the rest of EPP’s administrative
staff have given me.
Finally, I would like to thank my parents William and Patricia Katzenstein for their never-
ending support and love, my brothers Aaron and Wesley, my sister Julie, and good friends
Andres Del Campo, Ben Nahir, Shelby Suckow, Ryan and Kym Hallahan, Lee Gresham, and Brett
Bissinger for their moral support.

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Table of Contents
CHAPTER 1 - INTRODUCTION 1
1.1 OVERVIEW AND MOTIVATION 1
1.2 REFERENCES 4
CHAPTER 2 - THE VARIABILITY OF INTERCONNECTED WIND PLANTS 6
2.1 CHAPTER INFORMATION 6
2.2 ABSTRACT 6
2.3 INTRODUCTION 7
2.4 DATA 9
2.5 METHODS 13
2.5.1 INTERCONNECTING WIND PLANTS 13
2.5.2 MISSING DATA 14
2.5.3 SCALING WIND DATA TO HUB HEIGHT 15
2.5.4 CORRELATION ANALYSIS 15
2.5.5 STEP CHANGE ANALYSIS 16
2.5.6 FREQUENCY DOMAIN 17
2.5.7 WIND DROUGHT ANALYSIS 20
2.6 RESULTS 21
2.6.1 FREQUENCY DOMAIN 21
2.6.2 GENERATION DURATION CURVES 24
2.6.3 PAIRWISE CORRELATIONS OF WIND POWER OUTPUT 26
2.6.4 STEP CHANGE ANALYSIS 29
2.6.5 ARE THERE WIND DROUGHTS? 32
2.7 ANALYSIS 33
2.8 REFERENCES 34
2.9 APPENDIX A 37
CHAPTER 3 - THE COST OF WIND POWER VARIABILITY 40
3.2 ABSTRACT 40
3.3 INTRODUCTION 41
3.4 DATA 43
3.5 METHODS 43
3.6 RESULTS 48
3.7 CONCLUSIONS 55

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3.8 REFERENCES 58
3.9 APPENDIX B 60
CHAPTER 4 - AIR EMISSIONS DUE TO WIND AND SOLAR POWER 69
4.2 ABSTRACT 69
4.3 INTRODUCTION 70
4.4 MODEL 72
4.5 DATA 72
4.6 APPROACH 73
4.7 RESULTS 75
4.8 MULTIPLE TURBINE ANALYSIS FOR CO2 EMISSIONS RESULTS 80
4.9 INTERACTIONS BETWEEN RPSS AND CAIR 83
4.10 DISCUSSION 85
4.11 REFERENCES 87
4.12 APPENDIX C 89
4.12.1 REGRESSION ANALYSES 89
4.12.2 REGRESSIONS CONSTRAINTS 99
4.12.3 PROFILE SENSITIVITY ANALYSIS RAW DATA 101
4.12.4 MULTIPLE TURBINE ANALYSIS 104
CHAPTER 5 - CONCLUSION 106
5.1 SUMMARY OF RESULTS 106
5.2 FUTURE WORK 107
5.3 POLICY IMPLICATIONS 110

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List of Figures
FIGURE 1-1 - RECENT DEVELOPMENT OF WIND POWER IN THE UNITED STATES (WISER AND BOLINGER,
2009)...................................................................................................................................................... 3
FIGURE 2-1 - LOCATIONS OF THE ERCOT WIND PLANTS FROM WHICH DATA WERE OBTAINED................. 10
FIGURE 2-2 – LOCATIONS OF THE AIRPORTS FROM WHICH DATA WERE OBTAINED. ................................. 12
FIGURE 2-3 – POWER SPECTRAL DENSITY (WITH 8 SEGMENT AVERAGING, K = 8) FOR 1 WIND PLANT, 4
INTERCONNECTED WIND PLANTS, AND 20 INTERCONNECTED WIND PLANTS IN ERCOT. WIND
POWER VARIABILITY IS REDUCED AS MORE WIND PLANTS ARE INTERCONNECTED, WITH
DIMINISHING RETURNS TO SCALE. ...................................................................................................... 22
FIGURE 2-4 – FRACTION OF A KOLMOGOROV SPECTRUM OF 1 WIND PLANT FOR INTERCONNECTED WIND
PLANTS OVER A FREQUENCY RANGE OF 1.2X10
-5
TO 5.6X10
-4
HZ. AS MORE WIND PLANTS ARE
INTERCONNECTED LESS POWER IS CONTAINED IN THIS FREQUENCY RANGE. ................................... 23
FIGURE 2-5 - FRACTION OF A KOLMOGOROV SPECTRUM OF DIFFERENT TIME SCALES VERSUS THE
NUMBER OF INTERCONNECTED WIND PLANTS. INTERCONNECTING FOUR OR FIVE WIND PLANTS
ACHIEVES THE MAJORITY OF THE REDUCTION OF WIND POWER’S VARIABILITY. WE NOTE THAT
REDUCTIONS IN WIND POWER VARIABILITY ARE DEPENDENT ON MORE THAN JUST THE NUMBER OF
WIND PLANTS INTERCONNECTED (E.G. SIZE, LOCATION, AND THE ORDER IN WHICH THE WIND
PLANTS ARE CONNECTED; SEE EQUATION 2-9)................................................................................... 23
FIGURE 2-6 – NORMALIZED GENERATION DURATION CURVES FOR ERCOT INTERCONNECTED WIND
PLANTS AND BPA'S TOTAL WIND POWER FOR 2008. THE AVERAGE NORMALIZED GENERATION
DURATION CURVE OF ERCOT’S 20 WIND PLANTS INTERCONNECTED WITH THEIR NEAREST THREE
NEIGHBORS IS PLOTTED (DOTTED LINE) WITH THE AREA ENCOMPASSED BY ONE STANDARD
DEVIATION (TAN AREA). ...................................................................................................................... 26
FIGURE 2-7 - CORRELATION COEFFICIENTS VS. DISTANCE BETWEEN PAIRS OF WIND PLANTS (INSET SHOWS
THE DATA ON A SEMI-LOG PLOT). ....................................................................................................... 27
FIGURE 2-8 – ASOS STEP CHANGE ANALYSIS USING KCNK (CONCORDIA, KANSAS) AS THE STARTING
LOCATION. EACH POINT REPRESENTS AN ADDITIONAL INTERCONNECTED STATION. THE RELATIVE
MAXIMUM STEP CHANGE, MEASURED AS THE MAXIMUM STEP CHANGE DIVIDED BY THE MAXIMUM
POWER, DECREASES WITH DISTANCE AS MORE WIND PLANTS ARE INTERCONNECTED.................... 30
FIGURE 2-9 – ASOS STEP CHANGE ANALYSIS USING KMOT (MINOT, NORTH DAKOTA) AS THE STARTING
LOCATION. EACH POINT REPRESENTS AN ADDITIONAL INTERCONNECTED STATION. THE RELATIVE
MAXIMUM STEP CHANGE, MEASURED AS THE MAXIMUM STEP CHANGE DIVIDED BY THE MAXIMUM
POWER, DECREASES WITH DISTANCE AS MORE WIND PLANTS ARE INTERCONNECTED.................... 31
FIGURE 2-10 – ERCOT STEP CHANGE ANALYSIS WHEN WIND PLANT 1 (DELAWARE MOUNTAIN, TX) IS USED
AS THE STARTING LOCATION. THE RELATIVE MAXIMUM STEP CHANGE, MEASURED AS THE
MAXIMUM STEP CHANGE DIVIDED BY THE MAXIMUM POWER, DECREASES WITH DISTANCE AS
MORE WIND PLANTS ARE INTERCONNECTED. .................................................................................... 32
FIGURE 2-11 – NORMALIZED PREDICTED ANNUAL WIND ENERGY PRODUCTION FROM 16 WIND TURBINES
LOCATED THROUGHOUT THE CENTRAL AND SOUTHERN GREAT PLAINS. THE NORMALIZED ANNUAL
HYDROPOWER PRODUCTION FOR THE UNITED STATES IS ALSO PLOTTED FOR COMPARISON.......... 33
FIGURE 3-1 - CONCEPTUAL DIAGRAM OF HOW WE PARTITION WIND ENERGY INTO HOURLY ENERGY,
LOAD FOLLOWING, AND REGULATION COMPONENTS. ...................................................................... 46
FIGURE 3-2 - ESTIMATED VARIABILITY COSTS FOR 20 ERCOT WIND PLANTS VERSUS THEIR CAPACITY
FACTORS FOR 2008. THE VARIABILITY COST OF WIND POWER DECREASES AS THE CAPACITY FACTOR
OF A WIND PLANT INCREASES............................................................................................................. 49

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FIGURE 3-3 - VARIABILITY COSTS OF WIND ENERGY DECREASE AS WIND PLANTS ARE INTERCONNECTED.
INTERCONNECTING 20 WIND PLANTS TOGETHER PRODUCES A MEAN SAVINGS OF $3.76 PER MWH
COMPARED TO THE 20 INDIVIDUAL ERCOT WIND PLANTS (GREEN DOTS). ONLY 8 WIND PLANTS
NEED TO BE INTERCONNECTED TO ACHIEVE 74% OF THE REDUCTION IN VARIABILITY COST. THREE
CASES ARE SHOWN WHERE THE HIGHEST, MEDIAN, AND LOWEST VARIABILITY COST WIND PLANTS
WERE USED AS STARTING POINTS AND THE REMAINING 19 WIND PLANTS WERE INTERCONNECTED
TO THEM BASED ON DISTANCE (CLOSEST TO FARTHEST). .................................................................. 50
FIGURE 3-4 - MARGINAL BENEFIT OF INTERCONNECTING AN ADDITIONAL WIND PLANT IN REDUCING
VARIABILITY COSTS. FOR EXAMPLE, WITH ONE WIND PLANT INTERCONNECTED TO A SYSTEM, THE
MAXIMUM MARGINAL BENEFIT OF INTERCONNECTING ANOTHER WIND PLANT IS $3.43 PER MWH.
............................................................................................................................................................. 52
FIGURE 3-5 - MARGINAL BENEFIT OF INTERCONNECTING AN ADDITIONAL WIND PLANT VALUED IN TERMS
OF MILES ERCOT WOULD BE WILLING TO EXTEND A 2GW, 100 MILE TRANSMISSION LINE............... 54
FIGURE 3-6 - THE CHANGE IN WIND PLANT RANKING OF VARIABILITY COST FROM 2008 TO 2009. FOR
2008 (LEFT SIDE), WE RANKED THE 20 ERCOT WIND PLANTS BASED ON THEIR ESTIMATED
VARIABILITY COSTS AND ASSIGNED THE LABELS A THROUGH T TO THE 20 WIND PLANTS, WITH A
BEING THE WIND PLANT WITH THE HIGHEST VARIABILITY COST AND T BEING THE WIND PLANT WITH
THE LOWEST VARIABILTY COST. FOR 2009 (RIGHT SIDE), WE REORDERED THE WIND PLANTS BASED
ON THEIR VARIABILITY COSTS BUT KEPT THE LABELS THE SAME........................................................ 55
FIGURE 3-7 - LOCATION OF THE 20 ERCOT WIND PLANTS IN TEXAS............................................................ 60
FIGURE 3-8 - BOX PLOTS FOR 2004 ERCOT ANCILLARY SERVICE PRICES ..................................................... 61
FIGURE 3-9 - BOX PLOTS FOR 2005 ERCOT ANCILLARY SERVICE PRICES...................................................... 62
FIGURE 3-10 - BOX PLOTS FOR 2006 ERCOT ANCILLARY SERVICE PRICES.................................................... 62
FIGURE 3-14 - SENSITIVITY OF OUR 2008 WIND POWER RESULTS TO DIFFERENT YEARS OF ANCILLARY
PRICE DATA.......................................................................................................................................... 65
FIGURE 3-15 - SENSITIVITY OF OUR 2009 WIND POWER RESULTS TO DIFFERENT YEARS OF ANCILLARY
PRICE DATA.......................................................................................................................................... 65
FIGURE 3-16 - ACTUAL POWER CURVE FOR A WIND TURBINE .................................................................... 66
FIGURE 3-17 - CHANGE IN 2008 WIND PLANT RANKINGS BASED ON VARIABILITY COST FOR SIX DIFFERENT
YEARS OF ANCILLARY SERVICE PRICES................................................................................................. 67
FIGURE 3-18 - CHANGE IN 2009 WIND PLANT RANKINGS BASED ON VARIABILITY COST FOR SIX DIFFERENT
YEARS OF ANCILLARY SERVICE PRICES................................................................................................. 67
FIGURE 3-19 - CHANGE IN WIND PLANT RANKINGS WHEN THE ANCILLARY PRICE DATA IS HELD CONSTANT.
IN THE LEFT SUBPLOT, 2008 ANCILLARY PRICE DATA WAS USED WITH 2008 AND 2009 WIND POWER
DATA. IN THE RIGHT SUBPLOT, 2009 ANCILLARY SERVICE PRICES WERE USED WITH 2008 AND 2009
............................................................................................................................................................. 68
FIGURE 4-1 - MEAN RENEWABLE PLUS NATURAL GAS EMISSION FACTORS VS. RENEWABLE ENERGY
PENETRATION LEVELS (Α) (SOLID BLACK LINE); AREA SHOWN REPRESENTS 2 STANDARD DEVIATIONS
OF ALL FIVE DATA SETS (SHADED BROWN AREA); SEE FIGURE 4-2 FOR REPRESENTATIVE SINGLE DATA
SET VARIABILITY. THE EXPECTED EMISSIONS FACTOR (GREEN, LOWER LINE IN EACH FIGURE) IS
SHOWN FOR COMPARISON. (A) LM6000 CO2. (B) LM6000 NOX. (C) 501FD CO2. (D) 501FD NOX.... 78
FIGURE 4-2 - RENEWABLE PLUS GAS GENERATOR SYSTEM MEAN EXPECTED EMISSION REDUCTIONS (Η)
VS. VARIABLE ENERGY PENETRATION FACTORS (Α). 95% PREDICTION INTERVALS (DASHED LINES)

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ARE SHOWN ONLY FOR THE EASTERN WIND PLANT. (A) LM6000 CO2. (B) LM6000 NOX. (C) 501FD
CO2. (D) 501FD NOX.............................................................................................................................. 80
FIGURE 4-3 - FRACTION OF EXPECTED CO2 EMISSION REDUCTIONS ACHIEVED (Η) WHEN (A) 5
GENERATORS ARE USED TO COMPENSATE FOR WIND’S VARIABILITY, (B) 20 GENERATORS ARE USED,
(C) 5 GENERATORS AND ONE GENERATOR IS USED AS A SPINNING RESERVE, (D) 20 GENERATORS
AND ONE GENERATOR IS USED AS A SPINNING RESERVE. THE BLACK LINE REPRESENTS THE MEAN Η
AND THE AREA SHOWN (SHADED BROWN AREA) REPRESENTS ONE STANDARD DEVIATION FROM
THE MEAN WHEN THE SOUTHERN GREAT PLAINS WIND DATA SET IS USED...................................... 82
FIGURE 4-4 - LM6000 RAW NOX EMISSIONS DATA....................................................................................... 89
FIGURE 4-5 - LM6000 RAW CO2 EMISSIONS DATA....................................................................................... 90
FIGURE 4-6 - LM6000 EMISSIONS DATA. THE EMISSIONS DATA WERE DIVIDED INTO FOUR REGIONS
WHICH WERE MODELED INDEPENDENTLY. THE CONSTRAINT CURVES IMPOSED BY THE POPULATED
DATA ARE SHOWN FOR EACH REGION................................................................................................ 90
FIGURE 4-7 - ABSOLUTE PERCENT ERROR BETWEEN CALCULATED CO2 EMISSIONS BASED ON REGRESSIONS
AND ACTUAL CO2 EMSSIONS FROM LM6000 DATA SET...................................................................... 92
FIGURE 4-8 - ABSOLUTE PERCENT ERROR BETWEEN CALCULATED CO2 EMISSIONS BASED ON REGRESSIONS
AND ACTUAL CO2 EMISSIONS FROM LM6000 DATA SET. RESULTS ARE COLORED ACCORDING TO THE
REGIONS (FIGURE 4-6). TOP: ABSOLUTE PERCENT ERROR FOR EACH DATA POINT VERSUS POWER
LEVEL. BOTTOM: ABSOLUTE PERCENT ERROR FOR EACH DATA POINT VERSUS RAMP RATE............ 92
FIGURE 4-9 - CO2 EMISSIONS RATE FOR THE 501FD TURBINES AS A FUNCTION OF TURBINE OUTPUT
POWER (BLUE DOTS) AND THE LINEAR REGRESSION MODEL USED TO CHARACTERIZE THE CO2
EMISSIONS RATE (RED LINE). THE LINEAR REGRESSION EQUATION IS Y = 0.00184X + 0.118 AND HAS
AN ADJUSTED R
2
VALUE OF 0.991. ...................................................................................................... 94
FIGURE 4-10 - 501FD NOX EMISSIONS DATA AS A FUNCTION OF POWER (BLUE DOTS) AND REGRESSION
(RED LINE). THE EMISSIONS DATA WERE DIVIDED INTO THREE REGIONS WHICH WERE MODELED
INDEPENDENTLY OF EACH OTHER. THIS COMBINED-CYCLE TURBINE IS DESIGNED TO PRODUCE LOW
NOX ONLY WHEN OPERATED AT HIGH POWER................................................................................... 96
FIGURE 4-11 - ABSOLUTE PERCENT ERROR BETWEEN NOX EMISSIONS BASED ON REGRESSIONS AND
ACTUAL NOX EMISSIONS FROM LM6000 DATA SET............................................................................ 98
FIGURE 4-12 - ABSOLUTE PERCENT ERROR BETWEEN CALCULATED NOX EMISSIONS BASED ON
REGRESSIONS AND ACTUAL NOX EMISSIONS FROM LM6000 DATA SET. RESULTS ARE COLORED
ACCORDING TO THE REGIONS (FIGURE 4-6). TOP: ABSOLUTE PERCENT ERROR FOR EACH DATA
POINT VERSUS POWER LEVEL. BOTTOM: ABSOLUTE PERCENT ERROR FOR EACH DATA POINT VERSUS
RAMP RATE.......................................................................................................................................... 98
FIGURE 4-13 -501FD EMISSIONS DATA. THE BOUNDARIES ON THE MODEL'S RAMP RATE, IMPOSED BY THE
POPULATED DATA POINTS IN THE CONTROL MAP, ARE SHOWN. THE 501FD WAS OPERATED IN A
MANNER THAT SAMPLED MORE POINTS IN ITS CONTROL MAP THAN THE LM6000 AND AS A RESULT
THE 501FD MODEL IS NOT AS CONSTRAINED AS THE LM6000 MODEL. ........................................... 100
FIGURE 4-14 - 501FD CO2 EXPECTED EMISSIONS REDUCTION RAW RESULTS FROM PROFILE SENSITIVITY
ANALYSIS............................................................................................................................................ 102
FIGURE 4-15 - 501FD NOX EXPECTED EMISSIONS REDUCTION RAW RESULTS FROM PROFILE PENETRATION
ANALYSIS............................................................................................................................................ 103
FIGURE 4-16 - LM6000 CO2 EMISSIONS REDUCTION RAW RESULTS FROM PROFILE PENETRATION
ANALYSIS............................................................................................................................................ 103
FIGURE 4-17 - LM6000 NOX EXPECTED EMISSIONS REDUCTION RAW RESULTS FROM PROFILE
PENETRATION ANALYSIS.................................................................................................................... 104

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FIGURE 4-18 -501FD MULTIPLE TURBINE ANALYSIS USING THE EASTERN WIND DATA SET. BY PAIRING N
501FD TURBINES WITH A VARIABLE POWER PLANT, THE LOWER POWER LIMIT (PMIN) OF THE
TURBINES IS P - P/N MW. FOR 2 OR MORE TURBINES, PMIN IS GREATER THAN 50% OF THE 501FD’S
NAMEPLATE CAPACITY AND NOX EMISSIONS ARE REDUCED ACCORDING TO EXPECTATIONS. IF NO
ATTENTION IS PAID TO PMIN, NOX EMISSIONS INCREASE................................................................... 105

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List of Tables
TABLE 2-1 - TABLE OF ASOS STATIONS USED TO OBTAIN WIND SPEED DATA............................................. 37
TABLE 2-2 - ERCOT WIND PLANTS ................................................................................................................ 39
TABLE 3-1 - MEAN AND MEDIAN VALUES FOR ERCOT'S DOWN REGULATION (DR), UP REGULATION (UR),
AND BALANCING ENERGY SERVICE (BES) ............................................................................................ 61
TABLE 4-1 - BASELOAD POWER PLANT MODEL RESULTS FOR 5 VARIABLE RENEWABLE POWER PLANT DATA
SETS. NOTE THAT WITH NIGHT PERIODS REMOVED, THE DAY-ONLY CAPACITY FACTOR FOR THE
SOLAR PV PLANT WAS 45%. THE 95% PREDICTION INTERVALS ARE SHOWN FOR A LEAST SQUARES
MULTIPLE REGRESSION ANALYSIS (MENDENHALL, 1994)................................................................... 77
TABLE 4-2 - SUMMARY RESULTS OF CAIR ANALYSIS FOR THE 12 CAIR STATES WITH A RENEWABLES
PORTFOLIO STANDARD. THE WIND PENETRATION FRACTION IS THE LARGER OF THE FRACTION OF
THE STATE’S 2020 RPS REQUIREMENT THAT COULD BE FULFILLED BY WIND, OR CURRENTLY
INSTALLED WIND. THE CAIR ALLOWANCE IS THE 2015 ALLOWANCE. NOTE: FRACTIONS MAY NOT
MATCH EXACTLY DUE TO ROUNDING. ................................................................................................ 85
TABLE 4-3 - ADUJSTED R
2
VALUES FOR THE REGRESSOINS USED TO MODEL EACH REGION OF EACH
TURBINE AND POLLUTANT. ................................................................................................................. 91
TABLE 4-4 - LM6000 REGION CO2 REGRESSION RESULTS............................................................................. 93
TABLE 4-5 - 501FD REGION CO2 REGRESSION ANALYSIS RESULTS............................................................... 94
TABLE 4-6 - 501FD REGION NOX REGRESSION RESULTS............................................................................... 97
TABLE 4-7 - LM6000 REGION NOX REGRESSION RESULTS ............................................................................ 99
TABLE 4-8 - WIND AND SOLAR PHOTOVOLTAIC DATA SETS FROM UTILITY-SCALE SITES USED IN THE
ANALYSIS. THE MAXIMUM OBSERVED POWER OF SEVERAL OF THE POWER PLANTS EXCEEDED THEIR
NAMEPLATE CAPACITY; IN OTHER CASES THE NAMEPLATE CAPACITY WAS NOT REACHED DURING
THE PERIOD FOR WHICH DATA WERE OBTAINED. ............................................................................ 101

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Chapter 1 -Introduction
1.1 Overview and Motivation
The recent growth in wind power is transforming the operation of electricity systems by
introducing variability into utilities’ generator assets. Due to a lack of cost-effective storage
solutions, utilities must continually produce the amount of electricity consumed by their customers.
Utilities have traditionally relied on dispatchable generators1
to serve their customers’ ever
changing demand for electricity. Wind plants, on the other hand, are not dispatchable assets and
system operators are currently learning how to incorporate significant quantities of wind energy.
Wind was one of the first power sources harnessed by civilizations. The earliest known
sailing vessels date back to 4000 BC and the earliest known windmills (to pump water or grind grain)
date back to 2000 BC (Anderson, 2003; Hinrichs and Kleinbach, 2002). Windmills became prevalent
throughout civilized societies numbering over 8,000 in Holland and 10,000 in England in 1750. In
the United States, rural farmers used them extensively to pump water for their crops, grind flour,
and later provide electricity for their farms. Yet windmills were made obsolete with the
development of the steam engine and the Rural Electrification Act of 1936 (Hinrichs and Kleinbach,
2002).
The modern era of wind power started with the oil embargo of 1973 and the subsequent
energy crisis. It was during the high fuel prices of the 1970s that the United States and Europe were
suddenly aware of their dependence on foreign fuel supplies and they began efforts for energy
independence. The United States and Europe immediately responded by pouring tens of millions of
1
Generators such as fossil-fuel, nuclear, or hydro power plants that system operators can dispatch to provide
a certain amount of power at a certain amount of time.

2
dollars into the research and development of wind turbines to generate electricity (Righter, 1996).
Hindsight has shown the governments’ R&D effort was not a primary driver of innovation and that
federal subsidies were a better mechanism to spur innovation in wind turbine design (Samaras,
2006).
The United States needed to do more than just fund R&D if wind power was going to have a
chance. During the late 1970s, the Carter administration realized electric utilities in the United
States would not pursue renewable energy projects even if mature technology existed (Graves et al.,
2006). As a result, the United States enacted the Public Utilities Regulatory Policies Act of 1978
(PURPA)2
to encourage the development and deployment of cogeneration and green energy
technologies. PURPA enabled third parties to develop and operate power plants but restricted the
types of power plants to small (<80 MW) renewable energy and cogeneration projects. Today,
approximately 83% of the wind projects developed between 1980 and 2008 are owned by third
party power producers (Wiser and Bolinger, 2009). PURPA, thus, was a significant policy act that
was vital to the future build out of wind power.
Yet even with the R&D efforts and the implementation of PURPA, wind power was still in its
infancy during the 1970s and 1980s because it was not cost-competitive with conventional
dispatchable generators. The United States realized wind power needed subsidies to encourage
large-scale deployment. This was first observed in the early 1980s when the United States shifted its
focus from funding wind turbine R&D to providing wind power subsidies. Approximately 1.5 GW of
wind power was installed between 1980 and 1985 as a result (figure 1-1). The early federal
subsidies were allowed to expire as soon as the price of oil fell substantially in 1986 (Hinrichs and
Kleinbach, 2002). Federal subsidies for wind power were absent until 1994 when Congress
2
It was also designed to increase the efficiency of our electricity use.

3
implemented the Production Tax Credit (PTC). The PTC was a sizable subsidy and as seen in figure 1-
1, the wind power industry in the United States was dependent on the PTC. The US wind power
industry grew significantly when the PTC was in effect and much more slowly when the PTC expired
briefly in 2000, 2002, and 2004. Thus, the PTC was the final piece the US wind industry needed to
spur the modern increase in wind power in the United States.
Figure 1-1 - Recent development of wind power in the United States (Wiser and Bolinger, 2009)
As a result of the PTC and PURPA, wind grew at an average rate of 28% from 1998 to 2008
(EIA, 2009). Wind power penetration, in terms of energy, has gone from << 1% in 1997 to ~2% in
2009 in the United States (Wiser and Bolinger, 2009). The individual states in wind rich regions have
higher penetration rates. Lawrence Berkeley Laboratory estimates 15 states have wind energy
penetration rates > 2% with Iowa (13.3%), Minnesota (10.4%), and South Dakota (8.8%) as the three
states with the highest penetration levels (Wiser and Bolinger, 2009). Aggressive renewables
portfolio standards (RPS) enacted by 29 states and new federal and state subsidies are helping
ensure wind power maintains its aggressive growth for the next decade.

4
System operators are not experienced in utilizing significant quantities of variable power to
meet their loads. As a result, system operators have struggled at times to keep their systems stable.
The Electricity Reliability Council of Texas (ERCOT), for example, worked hard to keep their system
stable when it lost ~1.7 GW of wind power over a 4 hour period on February 26, 2008. The sudden
die-off of wind adversely coupled with an unanticipated rise in ERCOT’s load and forced ERCOT to
implement their Emergency Electric Curtailment Plant (EECP) to curtail 1200 MW of interruptible
load (ERCOT, 2008)3
. In another example, the wind in Bonneville Power Authority’s (BPA) territory
unexpectedly calmed for 12 days in January 2009 (BPA, 2009). As a result, BPA lost 1 GW of wind
power for a week and a half and was forced to use its hydro reserves in wind’s place.
System operators are learning in real-time how to incorporate wind power and its
variability. This thesis is meant to help system operators have a better understanding of wind
power variability and its implications for their electricity system. In Chapter 2, I present methods to
characterize large penetrations of wind power and measure reductions in wind power variability as
wind plants are interconnected in ERCOT. In Chapter 3, I present methods to estimate the cost of
wind power variability and value reductions in wind power variability. Finally, in Chapter 4, I
estimate what effect wind variability has on the emissions of fossil fuel generators and what
implications this has for emissions displacement calculations.
1.2 References
Anderson, R.C., 2003. A Short History of the Sailing Ship. Courier Dover, Mineola.
BPA, 2009. Integrating Wind Power and Other Renewable Resources into the Electricity Grid.
Bonneville Power Authority, September. Available:
http://www.bpa.gov/corporate/windpower/docs/Wind-
WIT_generic_slide_set_Sep_2009_customer.pdf
3
During the ERCOT incident 150 MW of conventional generation tripped offline and was a contributing factor
although a minor one compared to the loss of 1.7 GW of wind power and the addition of 4 GW of load.

5
EIA, 2009. Annual Energy Review – Table 8.2a Electricity Net Generation: Total (All Sectors), 1949-
2008. US Energy Information Agency. Available:
http://www.eia.doe.gov/emeu/aer/txt/stb0802a.xls
ERCOT, 2008. ERCOT Operations Report on the EECP Event of February 26, 2008. Electricity
Reliability Council of Texas. Available:
http://www.ercot.com/meetings/ros/keydocs/2008/0313/07._ERCOT_OPERATIONS_REPORT_EECP
022608_public.doc
Graves, F., Hanser, P., Basheda, G., 2006. PURPA: Making the Sequel Better than the Original.
Edison Electric Institute. Available:
http://www.eei.org/whatwedo/PublicPolicyAdvocacy/StateRegulation/Documents/purpa.pdf
Hinrichs, R., Kleinback, M., 2002. Energy: Its Use and the Environment. Harcourt, Orlando.
Righter, R., 1996. Wind Energy in America: A History. University of Oklahoma Press, Norman.
Samaras, C., 2006. Learning from Wind: A Framework for Effective Low-Carbon Energy Diffusion.
Carnegie Mellon Electricity Industry Center, Working Paper CEIC-06-05. Available:
http://wpweb2.tepper.cmu.edu/ceic/publications.htm
Wiser, R., Bolinger, M., 2009. 2008 Wind Technologies Market Report. Energy Efficiency and
Renewable Energy, US Department of Energy. Available: http://eetd.lbl.gov/ea/emp/reports/2008-
wind-technologies.pdf

6
Chapter 2 -The Variability of Interconnected Wind Plants
2.1 Chapter Information
Authors: Warren Katzenstein, Emily Fertig, and Jay Apt
Published: Aug 2010 in Energy Policy.
Citation: Katzenstein, W., Fertig, E., Apt, J., 2010. The Variability of Interconnected Wind Plants.
Energy Policy, 38(8), p.4400-4410.
2.2 Abstract
We present the first frequency-dependent analyses of the geographic smoothing of wind
power's variability, analyzing the interconnected measured output of 20 wind plants in Texas.
Reductions in variability occur at frequencies corresponding to times shorter than ~24 hours and are
quantified by measuring the departure from a Kolmogorov spectrum. At a frequency of 2.8x10-4
Hz
(corresponding to 1 hour), an 87% reduction of the variability of a single wind plant is obtained by
interconnecting 4 wind plants. Interconnecting the remaining 16 wind plants produces only an
additional 8% reduction. We use step-change analyses and correlation coefficients to compare our
results with previous studies, finding that wind power ramps up faster than it ramps down for each
of the step change intervals analyzed and that correlation between the power output of wind plants
200 km away is half that of co-located wind plants. To examine variability at very low frequencies,
we estimate yearly wind energy production in the Great Plains region of the United States from
automated wind observations at airports covering 36 years. The estimated wind power has
significant inter-annual variability and the severity of wind drought years is estimated to be about
half that observed nationally for hydroelectric power.

7
2.3 Introduction
Currently 29 of the United States of America have renewables portfolio standards (RPS) that
mandate increasing their percentage of renewable energy, and the US House of Representatives has
enacted a federal renewable electricity standard (Database of State Incentives for Renewables and
Efficiency, 2009; Waxman and Markey, 2009). Major electricity markets such as California, New
York, and Texas expect wind to play a large role in meeting their RPS. As a result of the state RPS
requirements and a federal production tax credit equivalent to a carbon dioxide price of
approximately $20/metric ton (Dobesova et al., 2005), wind power net generation is currently
experiencing very high growth rates (51% in 2008, 28% average annual growth rate over the past
decade) in the United States (EIA, 2009).
Wind power’s variability and fast growth rate have led areas including Cal-ISO, PJM, NY-ISO,
MISO, and Bonneville power to undertake wind integration studies to assess whether their systems
can accommodate significant (5-20%) penetrations of wind power (CAISO, 2007; DOE, 2008;
EnerNex, 2009; GE, 2008; Hirst, 2002). Included in each integration study is how wind power
variability can be mitigated with options such as storage, demand response, or fast-ramping gas
plants. Some system operators are beginning to charge wind operators for costs arising from the
integration of high wind penetration in their system. In 2009, the Bonneville Power Authority (BPA)
introduced a wind integration charge of $1.29 per kW per month (~0.6¢/kWh assuming a 30%
capacity factor), citing reliability risks and substantial costs encountered in fulfilling 7% of their
energy needs with wind power (BPA, 2009).
Previous studies have shown that interconnecting wind plants with transmission lines
reduces the variability of their summed output power as the number of installed wind plants and
the distance between wind plants increases (Archer and Jacobson, 2007; Czisch and Ernst, 2001;

8
Giebel, 2000; IEA, 2005; Kahn, 1979; Milligan and Porter, 2005; Wan, 2001). Kahn (1979) estimates
the increased reliability of spatially separated wind plants, writing that “wind generators can
displace conventional capacity with the reliability that has been traditional in power systems.”
Kahn (1979) calculates the loss of load probability (LOLP) and the effective load carrying capability
(ELCC) of up to 13 interconnected California wind plants.
Czisch and Ernst (2001) and Giebel (2000), in separate studies, show the correlation
between wind plants decreases with distance. Each concludes wind power variability is reduced by
summing the output power from spatially separated wind plants. Czisch and Ernst (2001) and Giebel
(2000) both find that wind plant outputs are correlated even over great distances (correlation
coefficient > 0).
Milborrow (2001) shows a smoothing effect by calculating the output power change over a
certain time interval (step-change) of wind plants. He finds the one-hour power swing of 1,860 MW
of wind power in Western Denmark over a three month period in 2001 was at most 18% of installed
capacity compared with 100% for a single wind plant. In contrast, Bonneville Power Authority in the
U.S. Pacific Northwest experienced a maximum one-hour step-change of 63% in 2008 for their 1,670
MW of wind power.
Archer and Jacobsen (2007) write that interconnected wind plants would produce “steady
deliverable power.” Using hourly and daily averaged wind speed measurements taken at 19 airports
located in Texas, New Mexico, Oklahoma, and Kansas, they estimate generation duration curves and
operational statistics of wind power arrays. They find that “an average of 33% and a maximum of
47% of yearly averaged wind power from interconnected plants can be used as reliable, baseload
electric power” (Archer and Jacobson, 2007).

9
The previous studies analyze wind’s variability primarily in the time domain, using metrics
such as 10-minute step-change histograms, correlation coefficients and LOLP.
Frequency domain analysis is a powerful complementary method that can be used to
characterize variability and evaluate whether and at what frequencies smoothing occurs as more
wind plants are introduced into a system. We use Fourier transform techniques to estimate the
power spectral density of wind generated power (PSD) (Apt, 2007; Cha and Molinder, 2006; Press et
al., 1992) and characterize the variability of actual wind plant output within ERCOT, the electricity
market serving most of Texas. We also use step-change analyses and correlation coefficients to
characterize the variability of ERCOT wind plants and wind plants modeled from wind monitoring
stations located throughout the Midwest and Great Plains and compare our results with previous
studies.
To characterize the year-to-year variations of wind power production, we calculate the
yearly output of wind power by modeling wind plants over a span of 36 years. We examine the
existence and likely severity of wind drought years as compared to hydroelectric power reduction by
rainfall droughts.
2.4 Data
We use both ERCOT wind plant power output data and National Oceanic and Atmospheric
Administration (NOAA) wind speed data for our analyses. We use 15-minute time resolution real
power output data from 20 wind plants within ERCOT (figure 2-1)4
. The ERCOT data were obtained
from ERCOT’s website and contained no dropouts. If necessary, data from each wind plant are
scaled to the end-of-the-year capacity of the wind plant to adjust for mid-year capacity additions.
4 Electric Reliability Council of Texas (2009) Entity-Specific Resource Output. Retrieved Feb. 18, 2009 from
ERCOT’s Planning and Market Reports. Available: http://www.ercot.com/gridinfo/sysplan/

10
We use 2008 wind power data from Bonneville Power Authority to examine whether results similar
to our ERCOT results are seen in another system. BPA provides 5-minute system wind power data
on its website5
. There were 0.04% of the data missing from BPA’s 2008 wind data set.
Figure 2-1 - Locations of the ERCOT wind plants from which data were obtained.
When examined in the frequency domain, ERCOT’s data exhibit the Kolmogorov spectrum of
wind plants as found by Apt (2007). The Nyquist frequency, the highest frequency the data can
represent without aliasing, is 5.6 x 10-4
Hz (corresponding to 30 minutes) for ERCOT’s 15-minute
wind power output data.
5 Bonneville Power Authority wind generation in balancing authority. Retrieved May 6, 2009. Available at
http://www.transmission.bpa.gov/business/operations/wind/

11
We use NOAA ASOS two-minute resolution wind speed data to estimate the effect of
interconnecting up to 40 wind plants throughout 7 states located in the Midwest, Southwest, and
Great Plains regions6
. ASOS is a joint project among NOAA, the Department of Defense, the Federal
Aviation Administration, and the US Navy with ~ 1000 stations that automatically record surface
weather conditions (NOAA et al., 1998). We selected 40 stations to represent the high wind energy
locations of the Great Plains region where wind plants are currently being developed; Archer and
Jacobson (2007) analyzed a subset of this region. Each minute, ASOS stations record wind speed
and direction averaged over the previous two minutes to the neared nautical mile per hour. Table
2-1 in appendix A lists the 40 ASOS sites we use and figure 2-2 plots their location. The average
distance between the 40 ASOS sites we use is 785 km and the median distance is 725 km.
6 See table 2-1 in the Appendix for a list of specific sites. Data are available at
ftp://ftp.ncdc.noaa.gov/pub/data/asos-onemin/

12
Figure 2-2 – Locations of the airports from which data were obtained.
There are three limitations to using ASOS wind speed data to model wind plants. The first is
that the data are reported as integer knots (NOAA et al., 1998). The second is that the data are a
running 2-minute average. Both reduce the high frequencies we can resolve in the frequency
domain (Over and D’Odorico, 2002). A noise floor is evident in the power spectral density, caused
by the one knot amplitude resolution of the data. The effect of averaging is a departure from the
Kolmogorov spectrum at frequencies greater than approximately 2x10-4
Hz (periods of 90 minutes or
shorter) that we do not observe in non-ASOS anemometer data. The third limitation of the ASOS

13
data set is prevalence of bad data7
. In 2007, our selected ASOS sites had an average bad data rate of
7.7%. Spencer Municipal Airport, Iowa (KSPW) had the best data collection in our sample with a bad
data rate of 4.6% and Theodore Roosevelt Regional Airport in Dickinson North Dakota (KDIK) had the
worst with a bad data rate of 16.5%.
We use NOAA hourly data obtained from airport sites (squares in figure 2-2) to study how
the energy output of wind plants varies over many years. There is significant variation in the
historical hourly data sets of the 40 airports prior to ASOS deployment in the 1990s. Some airports
recorded wind speeds every third hour and only during the day. Data dropouts of months to years
are present in the majority of the data sets. We used only the 16 airports out of the 40 that had
hourly wind speed data from 1973 to 2008 and did not have a data dropout greater than 5 days.
The 16 sites are listed in table 2-2 in appendix A and had an average missing data rate of 13%.
2.5 Methods
2.5.1 Interconnecting Wind Plants
We simulate wind plants interconnected with uncongested transmission capacity
(sometimes called the copper plate assumption) by summing together either ERCOT wind plant
power output data or NOAA airport wind speed data (taken at 8 or 10 meters, depending on the
station) scaled up to a height of 80 meters using a method outlined in section 2.5.3 and transformed
to power using a cubic curve (equation 2-1) that provides a good match to observed data from 1.5
MW turbines and turbine-mounted anemometer data.
7 Bad ASOS data were data dropout where periods of time were missing from the data set.

14
Equation 2-1
ܲሺ‫ݐ‬ሻ ൌ ൝
341 െ 277‫ݒ‬௪௜௡ௗ ൅ 62‫ݒ‬௪௜௡ௗ
ଶ
െ 2.5‫ݒ‬௪௜௡ௗ
ଷ
1500
0
if
‫ݒ‬௪௜௡ௗ ൒ 2.9 m/s and ‫ݒ‬௪௜௡ௗ ൏ 14 m/s
‫ݒ‬௪௜௡ௗ ൒ 14 m/s
‫ݒ‬௪௜௡ௗ ൏ 2.9 m/s
Previous work indicates that wind power variability can be reduced by either increasing the
number of wind plants or increasing the distance between wind plants. For our step change and
frequency analyses, we add stations together according to their location. We select an ERCOT wind
plant as the starting point, calculate the distance to each of the other stations using a WGS-84
ellipsoidal Earth, and sort the results from closest to farthest wind plant (Vincenty, 1975). We
simulate interconnected wind plants by adding the closest wind plant’s power to the system,
perform step change and PSD analyses, and repeat until all wind plants have been interconnected.
The same method is used to add ASOS stations together by distance.
2.5.2 Missing Data
The 1-minute ASOS and hourly NOAA data sets are incomplete. For the ASOS data, we treat
missing data as follows. If the length of the missing data segment is less than 3 minutes, then the
missing data are filled in by interpolating between the 2 closest points. Any missing data segments
longer than 3 minutes are excluded from the summed result.
For the NOAA hourly data set used for the wind drought analysis, any missing data segments
with a length of 3 hours or less are filled in by interpolating between the 2 closest points. Any
missing data segments with a length greater than 3 hours but less than 120 hours are filled in using
average wind speeds calculated from the previous four weeks for each hour of the day. We then
take the time of day average segment that coincides with the missing data segment and scale it to
match its boundaries with the boundaries of the surrounding good data segments. Any data set that
has a missing data segment longer than 120 hours is excluded.

15
2.5.3 Scaling Wind Data to Hub Height
The airport wind speed measurements were taken at heights of 8 to 10 meters and are
scaled up to 80 meters before being transformed to power data. We use a logarithmic velocity
profile to estimate wind speeds at a hub height of 80 meters (equation 2-2) (Seinfeld and Pandis,
2006). The logarithmic velocity profile assumes the surface layer is adiabatic. The logarithmic
velocity profile depends on a surface roughness length that characterizes the boundary layer near
the ASOS station; we use ‫ݖ‬଴ ൌ 0.03 meters.
Equation 2-2
‫ݑ‬‫כ‬തതതሺ80݉ሻ ൌ
‫ݑ‬‫כ‬
ߢ
ln
80
‫ݖ‬଴
where
‫ݑ‬‫כ‬ ൌ
ߢ‫ݑ‬ത‫כ‬ሺ݄௥ሻ
ln
݄௥
‫ݖ‬଴
݄௥ ൌ reference height
‫ݖ‬଴ ൌ surface roughness length
κ ~ 0.4 (von Karman constant)
2.5.4 Correlation Analysis
Correlation between power output time series of two wind plants can be quantified by
Pearson’s correlation coefficient:
Equation 2-3
ߩ ൌ
∑ ሺ௫೔ି௫ҧሻሺ௬೔ି௬തሻ೔
ఙೣఙ೤ඥ∑ ሺ௫೔ି௫ҧሻమ
೔ ඥ∑ ሺ௬೔ି௬തሻమ
೔
; (−1≤ρ≤1).
Power outputs of two wind plants that rise and fall in relative unison have ρ near one, and
little smoothing takes place. A correlation coefficient near zero indicates that wind power outputs
vary independently of each other. A negative correlation coefficient, although not seen in the data,

16
would indicate anticorrelation between wind power outputs such that high power output from one
wind plant is associated with low power output from the other; maximum smoothing would occur if
ρ = -1. Previous studies have shown that as the distance between wind plants increases, the
correlation between their outputs decreases. The standard deviation of summed time series signals
is dependent on the correlation between each individual time series signal (equation 2-4) (Giebel,
2000).
Equation 2-4
σsum
2
=
1
N2
σiσ jcorrij
j
∑
i
∑
2.5.5 Step Change Analysis
The most common time domain method used in wind power studies is a step change
analysis (see for example Wan, 2004, 2007) where the change in power for a given time step is
calculated and either reported as power (e.g. MW) or as a percentage of the rated capacity of a
wind plant (equation 2-5). We calculate step changes as a percentage of the maximum power
produced by a wind plant or summed plants (equation 2-6).
Equation 2-5
)()( tPtPP −+=∆ τ or 100
)()(
×
−+
=∆
CapacityNameplateP
tPtP
P
τ
Equation 2-6
100
)max(
)()(
×
−+
=∆
P
tPtP
P
τ
We calculate step changes at 30-minute, 60-minute and 1-day time intervals because they
are important to ancillary services and day-ahead electricity markets. We plot the maximum step

17
change observed versus the distance from the original starting wind plant to the next wind plant
interconnected.
2.5.6 Frequency domain
To characterize the smoothing of wind power’s variability as a function of frequency as wind
plants are interconnected, we analyze wind power in the frequency domain. Our results can be used
to help determine the most economical generation portfolio to compensate for wind’s variability.
For the Texas wind plant data, we compute the discrete Fourier transform of the time series of
output in order to estimate the power spectrum (sometimes termed the power spectral density or
PSD) of the power output of a wind plant.
One of the attributes of power spectrum estimation is that increasing the number of time
samples does not decrease the standard deviation of the PSD at any given frequency fk. In order to
take advantage of a large number of data points in a data set to reduce the variance at fk, the data
set may be partitioned into K time segments. The Fourier transform of each segment is taken and a
PSD constructed. The PSDs are then averaged at each frequency, reducing the variance of the final
estimate by the number of segments (and reducing the standard deviation by K/1 . The length of
a data set determines the lowest frequency that can be resolved and segmenting increases the
lowest frequency we are able to resolve in a signal by a factor of K (Apt, 2007; Press et al., 1992).
Since we wish to characterize wind power variability in the time range of current market operations
(24 hours to 15 minutes), the decreased ability to examine frequencies corresponding to very long
times is a small price to pay for the decreased variance.
A Fourier transform requires evenly sampled data points to transform a signal from the time
domain to the frequency domain. The Texas wind plant output data is complete for the time period
(2008) examined. However, the ASOS data has significant gaps. For example, the longest continuous

18
data segment for one ASOS station was 42 days and the longest coincident continuous data segment
of the 40 summed ASOS stations was 12 hours. The high percentage of missing data would limit our
frequency analysis in two ways. First, we would be able to use only the 12 hours of coincident
continuous good wind speed data. Second, we wouldn’t be able to use segmenting to reduce the
variability of the ASOS PSDs because the length of the coincident continuous good data is so short.
To overcome the limitations imposed by the high percentage of missing ASOS data we calculate
PSDs by using a Lomb periodogram instead of a periodogram estimated using a Fourier transform.
The Lomb periodogram (Lomb, 1976) was developed for use in intermittent astrophysics data
(equation 2-7) and does not require evenly sampled data points to calculate the PSD of a signal.
Instead of calculating the Fourier frequencies of a signal, it applies a least-squares fit of sinusoids to
the data to obtain the frequency components. The time delay component τ in equation 2-7 ensures
the frequencies produced by the Lomb periodogram are orthogonal to one another. We implement
the Lomb periodogram by using the algorithm of Press et al. (1992).
Equation 2-7 - Lomb Periodogram
PN (ω) =
1
2σ2
(hj − h)cosω(t j − τ)
j
∑[ ]
2
cos2
ω(t j − τ)
j
∑
+
(hj − h)sinω(t j − τ)
j
∑[ ]
2
sin2
ω(t j − τ)
j
∑










Subject to the constraint:
tan(2ωτ) =
sin2ωt jj
∑
cos2ωt jj
∑
In computing the PSDs, we use 8 segments for the ERCOT data and 32 segments for the
ASOS data to reduce the variability of using a year’s worth of data. The algorithm used to

19
implement the Lomb periodogram requires two factors, ofac and hifac, to be defined for each signal.
The first factor, ofac, is an oversampling factor that we set to 6 for ASOS data and 1 for ERCOT data.
The second factor, hifac, determines the highest frequency the algorithm is able to resolve. We
calculate hifac for each signal to produce the correct Nyquist frequency.
Kolmogorov (1941) proposed that the energy contained in turbulent fluids is proportional to
the frequency of the turbulent eddies present in the fluid, E α f β
, with β = - 5/3, and this result has
been widely verified in subsequent empirical studies (for example, Grant et al., 1961; Monin, 1967).
Apt (2007) has shown the power spectrum of a wind plant’s power output follows a Kolmogorov
spectrum between frequencies of 30 seconds and 2.6 days. We expect departures from Kolmogorov
of β < -5/3 if any smoothing occurs when wind plants are interconnected. As wind plants are
interconnected we estimate β by linearly regressing the log of the PSD of the summed wind power
between the frequencies of 1.2x10-5
to 5.6x10-4
Hz (24 hours to 30 minutes).
Kolmogorov’s relationship is valid for wind only for frequencies corresponding to times of
approximately 24 hours or less. It has been shown the spectra of wind speed turbulence flatten for
longer frequencies, indicating wind has constant energy in its lower frequencies (longer than a few
days) (Jang and Lee, 1998). We use a modified von Karman formulation (equation 2-8) for wind
speed turbulence spectrum to model the power spectrum of one wind plant over the frequency
range of 43 days to 30 minutes (Kaimal, 1972).
To estimate the smoothing arising from interconnecting wind plants, we determine if
departures from a Kolmogorov spectrum occur in the following manner. We fit equation 2-8 to the
PSD of a single wind plant to determine a value for B.

20
Equation 2-8
3/5
1
)( −
+
=
Bf
A
fPSD
As we add wind plants to the single wind plant, we fit equation 2-8 to the resulting summed PSD to
determine a value for A and produce an appropriately scaled single wind plant model PSD. We then
compare the slope of the log of the summed PSD to the -5/3 slope of the single wind plant model in
the Kolmogorov region between frequencies corresponding to 30 minutes and 24 hours. We
measure deviations from the spectrum of equation 2-8 by dividing the power contained in each
frequency of the summed PSD by the power estimated in each frequency of the single wind plant
model. If no smoothing occurs when wind plants are interconnected the result should be close to 1
for all frequencies. If there is a reduction in variability then there will be frequencies for which the
fraction is less than 1. Finally, we use a linear regression on the log of the fractions to display the
mean fraction response versus frequency.
2.5.7 Wind Drought Analysis
Analyzing long-term variations in wind power production is important for system planning. If
significant drought periods occur, system planners must ensure adequate resources and renewable
energy credits (RECs) are available to cover the wind power underproduction. Similarly, wind
production that is significantly above the long-term average may depress the market price for RECs
and increase the requirements for compensating power sources.
We use hourly NOAA data to estimate the yearly energy production of wind turbines from 1973
to 2008. We scale the wind speed measurements to 80 meter hub heights (see section 2.5.3) and
transform it to hourly power data with a power curve (see section 2.5.1). A surface roughness of

21
0.03 meters is assumed for all of the airports. For each year the hourly power data from all 16
turbines is summed and compared to the mean yearly power production for the 35 year period.
2.6 Results
2.6.1 Frequency Domain
In figure 2-3, we show the ERCOT PSD results for 1, 4, and 20 wind plants using 15 minute
time resolution data for 2008. A single wind plant follows a Kolmogorov spectrum (f -5/3
) from
1.2x10-5
to 5.6x10-4
Hz (corresponding to times of 24 hours to 30 minutes). When 4 wind plants are
added together, the power contained in this region decreases with frequency at a faster rate ( f -2.49
instead of f -1.67
). For 20 wind plants the power decreases even more rapidly with increasing
frequency (f -2.56
). Adding wind plants together does not appreciably reduce the 24 hour peak.
BPA’s summed wind power (f -2.2
) shows less smoothing than ERCOT’s wind power, very likely
because 17 of BPA’s 19 wind plants are located within 170 km of each other in the Columbia River
gorge and the maximum distance between BPA wind plants is 290 km.

22
Figure 2-3 – Power spectral density (with 8 segment averaging, K = 8) for 1 wind plant, 4
interconnected wind plants, and 20 interconnected wind plants in ERCOT. Wind power variability
is reduced as more wind plants are interconnected, with diminishing returns to scale.
The amplitude of variability of twenty interconnected wind plants has ~95% less power at a
frequency of 2.8x10-4
Hz (corresponding to 1 hour) than that of a single wind plant (figure 2-4). The
reduction in variability has very rapidly diminishing returns to scale, as interconnecting 4 wind plants
gives an 87% reduction in variability at this frequency and interconnecting the remaining 16 wind
plants produces the remaining 8% reduction. The maximum reductions in variability occur at the
higher frequencies and dimish as the frequency decreases until at 24 hours there is no reduction in
variability (figure 2-3). Figure 2-5 shows the reduction in variability achieved as a function of the
number of interconnected wind plants for frequencies corresponding to 1, 6, and 12 hours.
10
-7
10
-6
10
-5
10
-4
10
-3
10
-4
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
Frequency (Hz)
PowerSpectralDensity
5 Days 24 Hours 1 Hour
↓ ↓ ↓
6 Hours
↓
1 Wind Plant
4 Wind Plants
20 Wind Plants

23
Figure 2-4 – Fraction of a Kolmogorov spectrum of 1 wind plant for interconnected wind plants
over a frequency range of 1.2x10-5 to 5.6x10-4 Hz. As more wind plants are interconnected less
power is contained in this frequency range.
Figure 2-5 - Fraction of a Kolmogorov spectrum of different time scales versus the number of
interconnected wind plants. Interconnecting four or five wind plants achieves the majority of the
reduction of wind power’s variability. We note that reductions in wind power variability are
dependent on more than just the number of wind plants interconnected (e.g. size, location, and
the order in which the wind plants are connected; see equation 2-9).
10
-5
10
-4
10
-3
0.1
1
← 2 wind plants
← 3
← 4
← 10
← 20
Frequency (Hz)
FractionofKolmogorovSpectrumof1WindPlant
24 Hours
↓
6 Hours
↓
1 Hour
↓

24
We calculate β (f β
) for simulations where each of ERCOT’s 20 wind plants is used as the
starting location and the remaining 19 wind plants are interconnected to it in order of their distance
(closest to farthest). We use the resulting 400 data points to model the change in β due to three
factors: ρ, the correlation coefficient between the interconnected wind plants and the next wind
plant to be interconnected; PNameplate Ratio, the ratio between the nameplate capacity of the wind
plant to be interconnected and the nameplate capacity of the interconnected wind plants; and N,
the number of wind plants interconnected. Equation 2-9 is the result of linearly regressing the log of
the change in β with the three variables (R2
is 0.77 and all variables are significant to a 99% level).
Equation 2-9
log ∆ߚ ൌ 7.6ߩ ൅ 0.91ܲே௔௠௘௣௟௔௧௘ ோ௔௧௜௢ െ 0.1ܰ െ 8.9
The PSD of forty interconnected modeled 1.5 MW GE turbines located throughout the Great
Plains and Midwest did not depart from a Kolmogorov spectrum. We have eliminated as a possible
cause the different time resolutions by averaging the ASOS data at 15 minute intervals (the ERCOT
sampling rate). It is possible that the discrepancy between the ASOS simulated power output and
the observed ERCOT power output spectra may arise from intra-wind-plant aerodynamic effects, but
further analysis is required, including the determination of the frequency dependence of the
smoothing as a function of wind plant size.
2.6.2 Generation Duration Curves
We have computed normalized generation duration curves for a single ERCOT wind plant,
twenty interconnected ERCOT wind plants, and all of BPA’s wind plants (figure 2-6). Also shown is
the average normalized generation duration curve of ERCOT’s 20 wind plants interconnected with
their nearest three neighbors and the area encompassed by +/- 1 standard deviation. One wind

25
plant has a higher probability of achieving close to its nameplate capacity than interconnected wind
plants but an increased probability of no wind or low wind power events.
Archer and Jacobson (2007) concluded on the basis of meteorological data that
interconnected wind plants spread throughout Texas, Oklahoma, Kansas, and New Mexico would
produce at least 21% of their rated capacity 79% of the time and 11% of their rated capacity 92% of
the time. The ERCOT and BPA data from operating wind turbines do not support that conclusion.
ERCOT’s twenty interconnected wind plants produced at least 10% of their rated power capacity
79% of the time and at least 3% of their rated capacity 92% of the time. BPA’s nineteen
interconnected wind plants produced at least 3% of their rated capacity 79% of the time and 0.5% of
their rated capacity 92% of the time. Hereinafter we define "firm power" for a generator as an
availability range of 79 to 92%.
Archer and Jacobson’s (2007) simulations produce baseload capacity equivalents for wind
power that are 2 to 20 times greater than those observed in the ERCOT and BPA data. Two effects
may be responsible for the discrepancy between our results and Archer and Jacobson’s results. The
first is that Archer and Jacobson analyze a larger geographical area than that encompassed by
ERCOT or BPA. The second is that Archer and Jacobson use individual model wind turbines while we
use data from operating wind plants.
The average generation duration curve of four interconnected ERCOT wind plants shows
that a small number of interconnected wind plants achieves the majority of the smoothing of wind
power’s variability and corresponds to the result obtained from our power spectral density analysis.
19 BPA and 20 ERCOT interconnected wind plants similarly achieve only 70% to 88% of their
nameplate capacities but BPA’s wind power has a higher probability of low to no wind power

26
occurances. The higher probability of low to no wind events in BPA’s system is likely because of the
limited geographic dispersion of BPA’s wind plants noted in the preceding section.
Figure 2-6 – Normalized generation duration curves for ERCOT interconnected wind plants and
BPA's total wind power for 2008. The average normalized generation duration curve of ERCOT’s
20 wind plants interconnected with their nearest three neighbors is plotted (dotted line) with the
area encompassed by one standard deviation (tan area).
2.6.3 Pairwise Correlations of Wind Power Output
In figure 2-7 we show the correlation coefficients between pairs of wind plants versus the
geographical distance between the wind plants, using measured 15-minute wind power averages
from 20 wind plants in Texas for 2008. Wind plants that are located less than 50 kilometers apart
tend to have highly correlated power outputs (0.7 < ρ < 0.9), while wind plants located more than
500 kilometers apart show lower correlation (ρ < 0.3). All of the correlation coefficients were
greater than zero at the 99% significance level (t-test).
10 20 30 40 50 60 70 80 90 100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Hours in a Year (%)
NormalizedPower
One ERCOT Wind Plant
Average of Four Interconnected ERCOT Wind Plants +/- 1 standard deviation
Average Four Interconnected Wind Plants
20 Interconnected ERCOT Wind Plants
BPA Wind Power

27
Figure 2-7 - Correlation coefficients vs. distance between pairs of wind plants (inset shows the
data on a semi-log plot).
The exponential fit shown in figure 2-7, ρ ∝exp(−distance/D), has a decay parameter D of
305 kilometers and an intercept of ρ = 0.89 at zero separation distance. A linear regression of log-
transformed correlation coefficients against distance has an R2
of 0.55 (i.e. the exponential model
explains about half of the variation in the correlation coefficients).
Eight pairs of wind plants, between 200 and 300 kilometers apart, have correlation
coefficients lower than 0.2 that lie below the overall trend. These eight pairs are Delaware
Mountain and Kunitz paired with each of Woodward Mountain, Indian Mesa, Southwest Mesa, and
King Mountain (table 2-2 – appendix A). This probably reflects the influence of local topography and
climate patterns and demonstrates that geographical proximity does not necessarily imply high
correlation. Removing these eight points increases D to 320 kilometers; the difference between this
value and that of the full data set is not statistically significant (t-test, 95% significance level), so the
cluster of 8 points does not exert strong leverage on the model.

28
Giebel (2000) performed a similar analysis for wind power in Europe and found D to be 641
kilometers (green line in figure 2-7). While the current study analyzes 15-minute wind energy data
sampled constantly for 2008, Giebel (2000) acquired data by applying a power curve to 10-minute
wind speed averages sampled every 3 hours, thus obtaining 10-minute wind power averages at 3-
hour intervals. To assess the distortion in cross-correlations that this difference introduces, one
week of 10-second wind power data for two wind plants in Texas and Oklahoma was processed to
mimic Giebel’s data as well as that of the current study. The correlation coefficient for 10-minute
averages taken every three hours was 0.31, and for consecutive 15-minute averages was also 0.31.
The similarity of these values suggests that the difference in data sampling frequencies between the
current study and Giebel (2000) does not introduce distortions that prohibit comparison.
Fixing the best-fit intercept for the Texas data in figure 2-7, the decay parameter of the
European model (641 km) differs from that of the best-fit Texas model (305 km) at the 99%
significance level (t-test). The R2
of Giebel’s model applied to the Texas data is 0.05, which reflects
the poor fit of the European model to the Texas data.
A significantly higher decay parameter for wind power in Texas would imply that more
smoothing occurs over a given distance in Texas than in Europe; however, large variation in
correlation coefficients for the European data prohibits a firm comparison. European wind speed
cross-correlation data for December 1990 – December 1991 has an exponential best fit with D = 723
kilometers (Giebel, 2000). The correlation coefficients show a large degree of scatter, especially in
the 0 – 500 kilometer region that overlaps with the data of the current study; between 400 and 500
kilometers, ρ for the European wind speed data ranges from approximately 0.1 to 0.7, while ρ for
the Texas wind power data ranges from 0.1 to 0.3. Assuming a similar degree of scatter in ρ for the
resulting European wind power time series, no significant difference between cross-correlations of

29
Texas and European wind power data can be determined by comparing the current study and Giebel
(2000); the European exponential model is a poor fit for the Texas data, but the Texas model could
fit the European data comparably to the best fit model of Giebel (2000), especially at distances
below 500 kilometers.
2.6.4 Step Change Analysis
Figure 2-8 shows the maximum ASOS 30-minute, 60-minute and 1-day percent step changes
in power as a function of distance when KCNK (Concordia, Kansas), a station close to the geographic
centroid of the ASOS airports, is used as the starting station, and additional stations are added
based on their distance from the starting station. Figure 2-9 is constructed using KMOT (Minot,
North Dakota), the station farthest from the geographical center of mass, as the starting station.
Adding together wind plants reduces the substantial step changes in power experienced by
individual wind plants. As more distant wind plants are interconnected, the maximum step change
in power relative to the maximum power produced reaches an asymptote of 15%-30% for step
changes of an hour or less. The reductions in variability are approximately equal to those observed
by Milborrow (2001) (a maximum hourly step-change of 18%) and are less than what BPA
experienced in 2008 (a maximum hourly step-change of 63%). BPA’s control area is significantly
smaller than the geographic region spanned by the 40 ASOS sites. The largest 30-minute increase or
decrease in power estimated from 40 interconnected ASOS wind plants was 15% of the maximum
wind power produced. The maximum 1-day step changes are also reduced as more distant wind
plants are interconnected although a reduction of at most 20% is achieved.
The reductions are obtained over relatively short distances with ~50% of the reductions
occurring within 400 km. In figure 2-8, 93% of the reductions occur in the first 600 km and 7%

30
occurs between distances of 600 to 1200 km. If the reference wind plant is at a geographic extreme
rather than the centroid (figure 2-9), 93% of the reductions occur in the first 1000 km.
Figure 2-8 – ASOS step change analysis using KCNK (Concordia, Kansas) as the starting location.
Each point represents an additional interconnected station. The relative maximum step change,
measured as the maximum step change divided by the maximum power, decreases with distance
as more wind plants are interconnected.
0 200 400 600 800 1000 1200 1400 1600 1800 2000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Distance (km)
RelativeMaximumStepChange
(MaximumStepChange/MaximumPower)
1-day up
1-day down
60-minute up
60-minute down
30-minute up
30-minute down

31
Figure 2-9 – ASOS step change analysis using KMOT (Minot, North Dakota) as the starting location.
Each point represents an additional interconnected station. The relative maximum step change,
measured as the maximum step change divided by the maximum power, decreases with distance
as more wind plants are interconnected.
Figure 2-10 shows the maximum ERCOT 30-minute, 60-minute, and 1-day percent step
changes in power when ERCOT wind plant 1 (Delaware Mountain), the wind plant farthest from the
geographic centroid of ERCOT’s wind plants, is used as the starting wind plant. Similar reductions in
variability to those simulated from ASOS data are produced when ERCOT wind plants are
interconnected. Reductions of 42% for 30-minute step changes, 50% for 60-minute step changes,
and 16% for 1-day step changes are achieved when wind plants within 500 km are interconnected.
The reductions for ERCOT are observed over shorter distances than predicted by the ASOS results.
In ERCOT’s system, wind power ramps up faster than it ramps down for each of the step change
intervals analyzed. If system operators are to match wind’s fluctuations exactly, they will need to
have a larger capacity from generators and demand response to ramp down their power than they
will require from them to ramp up.
0 200 400 600 800 1000 1200 1400 1600 1800 2000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Distance (km)
1-day up
1-day down
60-minute up
60-minute down
30-minute up
30-minute down

32
Figure 2-10 – ERCOT step change analysis when wind plant 1 (Delaware Mountain, TX) is used as
the starting location. The relative maximum step change, measured as the maximum step change
divided by the maximum power, decreases with distance as more wind plants are interconnected.
2.6.5 Are There Wind Droughts?
We estimated yearly variation in wind energy production from modeled 1.5 MW turbines at
16 locations over the years 1973 to 2008 (figure 2-11). Also plotted is the annual energy produced
from hydroelectric power in the United States for the same time span. We normalized each of the
results by their mean. The standard deviation for the estimated wind production was 6% of the
mean energy produced per year. The largest deviation from the mean occurred in 1988 when the
estimated wind energy production was 14% more than the mean annual production. The largest
negative deviation from the mean occurred in 1998 when estimated wind energy produced was 10%
less than the mean annual production. The standard deviation for the actual hydroelectric
production was 12% of the mean energy produced per year for the 36 year period. U.S.
hydropower’s largest positive deviation from the mean occurred in 1997 when hydropower
0 200 400 600 800 1000 1200 1400 1600 1800 2000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Distance (km)
1-day up
1-day down
60-minute up
60-minute down
30-minute up
30-minute down

33
production was 26% above the mean. The largest negative deviation occurred in 2001 when
hydropower production was 23% below average.
Thus, yearly wind energy production from the sample of 16 airports in the central and
southern Great Plains is predicted to exhibit long term variations, and these are about half that
observed nationally for hydropower (we note that the bulk of hydropower production is regionally
concentrated).
Figure 2-11 – Normalized predicted annual wind energy production from 16 wind turbines
located throughout the Central and Southern Great Plains. The normalized annual hydropower
production for the United States is also plotted for comparison.
2.7 Analysis
The variability of interconnected wind plants is less than that of individual wind plants when
measured in the time domain with step change analyses and in the frequency domain with power
spectrum analyses. The amount of smoothing is a predictable function of frequency, correlation
coefficient, nameplate capacity ratio, and the number of interconnected wind plants. Reductions in
variability diminish as more wind plants are interconnected. Finally, yearly wind power production
1970 1975 1980 1985 1990 1995 2000 2005 2010
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Year
NormalizedAnnualEnergyProduced
Estimated Wind Power Production for Central and Southern Great Plains
Hydropower Production for United States

34
is likely to vary, and have year-to-year variations about half that observed nationally for
hydropower.
These results do not indicate that wind power can provide substantial baseload power simply
through interconnecting wind plants. ERCOT’s generation duration curve shows wind power reliably
provides 3-10% of installed capacity as firm power (as defined above) while BPA’s generation
duration curve shows 0.5-3% of their wind power is firm power. The frequency domain analyses
have shown that the power of interconnected wind plants will vary significantly from day to day and
the results of the step change analyses show day-to-day fluctuations can be 75 to 85% of the
maximum power produced by a wind plant (figures 2-8 to 2-10).
The benefit of interconnecting wind plants is a significant reduction in the high frequency
variability of wind power. Reductions in the relative magnitude of the 30-minute and hourly step
changes will reduce the per MWh ancillary service costs of wind energy. The reductions will also
improve the root mean square error of wind energy forecasts for a system’s total wind energy
production but not the forecast error for individual wind plants. Estimating the value of these
benefits is difficult due to the proprietary algorithms used by system operators. We have provided
system planners with a metric that better characterizes the variability of large penetrations of wind
power. System planners can then identify the resources needed to compensate the variability and
calculate the associated costs.
2.8 References
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Archer, C.L., Jacobson, M.Z., 2007. Supplying baseload power and reducing transmission
requirements by interconnecting wind plants. Journal of Applied Meteorology and Climatology, 46,
1701-1717.

35
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Energy Association, Washington, DC, 2001. Available: http://www.iset.uni-kassel.de/abt/FB-
I/projekte/awea_2001_czisch_ernst.pdf
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abatement policy? Environmental Science & Technology, 2005. 39(22): 8578-8583.
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Renewable Energy. Available: http://www1.eere.energy.gov/windandhydro/pdfs/41869.pdf
DSIRE. Database of State Incentives for Renewables and Efficiency, 2009. www.dsireusa.org.
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2008. U.S. Energy Information Agency. Available:
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EnerNex, 2006. 2006 Minnesota wind integration study, Volume 1. EnerNex Corporation. Available:
http://www.uwig.org/windrpt_vol%201.pdf
ERCOT, 2009. Entity-Specific Resource Output. Retrieved Feb. 18, 2009 from ERCOT’s Planning and
Market Reports. Available: http://www.ercot.com/gridinfo/sysplan/
GE, 2008. ERCOT wind impact integration analysis. General Electric. Available:
http://www.ercot.com/meetings/ros/keydocs/2008/0227/ERCOT_final_pres_d1_w-o_backup.pdf
Giebel, G., 2000. On the benefits of distributed generation of wind energy in Europe. Ph.D.
dissertation, Carl von Ossietzky University of Oldenburg, 2000, 104 pp. Available:
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Grant, H.L., Stewart, R.W., Moilliet, A., 1961. Turbulence spectra from a tidal channel. Journal of
Fluid Mechanics, 12, 241-263.
Hirst, E., 2002. Integrating wind energy with the BPA power system: preliminary study. Bonneville
Power Authority. Available: http://www.bpa.gov/Power/pgc/wind/Wind_Integration_Study_09-
2002.pdf
International Energy Agency, 2005. Variability of Wind Power and Other Renewables –
Management Options and Strategies. Available: http://www.iea.org/papers/2005/variability.pdf

36
Jang, J., Lee, Y., 1998. A study of along wind speed power spectrum for Taiwan area. Journal of
Marine Science and Technology, 6.1, 71-77.
Kahn, E., 1979. The reliability of distributed wind generation. Electric Power Systems Research, 2, 1-
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Kaimal, J.C., 1972. Spectral characteristics of surface layer turbulence. Journal of the Royal
Meteorological Society, 98, 563-589.
Kolmogorov, A., 1941. The local structure of turbulence in incompressible viscous fluids at very
large Reynolds numbers. Dokl. Akad. Nauk. SSSR, 30, 301-305. Reprinted (1991) R. Soc. Lond.
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Milborrow, D, 2001. Penalties for intermittent sources of energy. Working Paper for U.K. Cabinet
Performance and Innovation Unit (PIU) Energy Review. Available:
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Renewable Energy Laboratory, Conference Paper, NREL/CP-500-38062. Available:
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Guide. Available: http://www.nws.noaa.gov/asos/pdfs/aum-toc.pdf
Over, T.M., D’Odorico, P., 2002. Scaling of surface wind speed. In : Lee, Jeffrey A. and Zobeck, Ted
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http://www.csrl.ars.usda.gov/wewc/icarv/15a.pdf
Press, W.H., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in FORTRAN: The
Art of Scientific Computing, second ed., Cambridge University Press, Cambridge, 1992.
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37
Wan, Y., 2004. Wind power plant behaviors: analyses of long-term wind power data. National
Renewables Energy Laboratory, Technical Report, NREL/TP-500-36551. Available:
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States House of Representatives, 111th
Congress. Available:
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2.9 Appendix A
Table 2-1 - Table of ASOS stations used to obtain wind speed data.
Station State
Latitude Longitude Hourly
Data
Used?Degrees Minutes Seconds Degrees Minutes Seconds
KEST IA 43 24 29.73 94 44 47.94
KSPW IA 43 9 57.64 95 12 20.15
KMCW IA 43 9 34.76 93 20 12.56 Yes
KAMW IA 41 59 59.49 93 37 16.3
KALO IA 42 33 22.35 92 23 47.19
KDDC KS 37 46 0.28 99 57 58.68 Yes
KGCK KS 37 55 43.6 100 43 32.48
KCNK KS 39 32 57 97 39 8 Yes
KRSL KS 38 52 16.67 98 48 31.04
KAAO KS 37 44 51.3 97 13 16
KEMP KS 38 19 55.34 96 11 18.26
KGLD KS 39 22 17.239 101 41 56.371 Yes
KICT KS 37 38 59.8 97 25 59 Yes
KRWF MN 44 32 48.41 95 5 0.09
KRST MN 43 54 31.73 92 29 48.18 Yes
KFCM MN 44 49 42.71 93 27 37.5
KAXN MN 45 51 56.85 95 23 32.27 Yes
KBIS ND 46 46 23.07 100 44 58.21 Yes

38
KJMS ND 46 55 44.34 98 40 41.91
KDIK ND 46 47 46.94 102 48 1.33 Yes
KMOT ND 48 15 33.78 101 16 51.9 Yes
KFAR ND 46 55 17.62 96 48 49.63 Yes
KCAO NM 36 26 43.89 103 9 14.13
KLVS NM 35 39 15.2 105 8 32.6
KCSM OK 35 20 26.74 99 11 55.82
KFDR OK 34 21 7.5449 98 59 2.0727
KGAG OK 36 17 43.94 99 46 35.125
KHBR OK 34 59 28.7 99 3 5
KPWA OK 35 32 3 97 38 49
KOKC OK 35 23 35.12 97 36 2.64 Yes
KABI TX 32 24 23.49 99 41 0.66 Yes
KAMA TX 35 13 8.52 101 42 18.84 Yes
KCDS TX 34 25 58.79 100 17 35.28
KDHT TX 36 1 20.41 102 32 58
KGDP TX 31 42 3.6 106 16 34.36
KLBB TX 33 39 48.86 101 49 22.18 Yes
KMAF TX 31 56 42.98 102 12 15.65 Yes
KODO TX 31 55 18.52 102 23 10.74
KINK TX 31 46 46.69 103 12 10.28
KSPS TX 33 59 19.666 98 29 30.816

39
Table 2-2 - ERCOT wind plants
Number Name Latitude Longitude
1 Delaware Mountain 31.6486 -104.75
2 Woodward 30.9575 -102.377
3 Indian Mesa 30.9333 -102.182
4 Southwest Mesa 31.0844 -102.108
5 King Mountain 31.2213 -102.161
6 Kunitz 31.3478 -104.4723
7 Capricorn Ridge 31.8207 -100.793
8 Airtricity 32.0649 -101.536
9 Sweetwater 32.32 -100.4
10 Trent Mesa 32.429 -100.199
11 Buffalo Gap 32.2287 -100.062
12 Horse Hollow 32.344 -99.9853
13 Callahan Divide 32.299 -99.872
14 Post Oak 32.7234 -99.2963
15 Mesquite 32.7234 -99.2963
16 Camp Springs 32.7556 -100.698
17 ENA Snyder 32.7921 -100.918
18 Brazos 32.9574 -101.128
19 Red Canyon 32.9389 -101.316
20 Whirlwind 34.0862 -101.086

40
Chapter 3 -The Cost of Wind Power Variability
3.1 Chapter Information
Authors: Warren Katzenstein and Jay Apt
Status: CEIC working paper
3.2 Abstract
We develop a metric to quantify the sub-hourly variability cost of individual wind plants and
show its use in valuing reductions in wind power variability. Our method partitions wind energy into
hourly and sub-hourly components and uses corresponding market prices to determine the cost of
variability. The metric is applicable to variability at all time scales faster than hourly, and can be
applied to long-period forecast errors. We use publically available data at 15 minute time resolution
to apply the method to ERCOT, the largest wind power production region in the United States. The
range of variability costs arising from 15 minute to 1 hour variations (termed load following) for 20
wind plants in ERCOT was $6.79 to 11.5 per MWh (mean of $8.73 ±$1.26 per MWh) in 2008 and
$3.16 to 5.12 per MWh (mean of $3.90 ±$0.52 per MWh) in 2009. Load following variability costs
decrease as wind plant capacity factors increase, indicating wind plants sited in locations with good
wind resources cost a system less to integrate. Twenty interconnected wind plants have a variability
cost of $4.35 per MWh in 2008. The marginal benefit of interconnecting another wind plant
diminishes rapidly: it is less than $3.43 per MWh for systems with 2 wind plants already
interconnected, less than $0.7 per MWh for 4-7 wind plants, and less than $0.2 per MWh for 8 or
more wind plants. This method can be used to value the installation of storage and other
techniques to mitigate wind variability.

41
3.3 Introduction
Wind power is quickly becoming a significant source of energy in the United States. It had
an average annual growth rate of 28% over the past decade and supplied 1.3% of United States’
energy in 2008 (EIA, 2010). However, wind is a variable source of power and increases the
operational costs of electricity systems because system operators are required to “secure additional
operating flexibility on several time scales to balance fluctuations and uncertainties in wind output”
(Northwest Wind Integration Action Plan, 2007). There is interest in using storage technologies or
fast-ramping fossil fuel generators, called flexible resources, to mitigate wind power variability and
decrease the costs of integrating wind power into electrical systems (Denholm, 2005; Hittinger et al.,
2010; Korpass et al., 2003).
Previous research and wind integration studies performed by Independent System
Operators (ISOs) and Regional Transmission Operators (RTOs) have estimated that the cost of
integrating wind power ranges from $0.5 to 9.5 per MWh for wind penetration levels ranging from
3.5 to 33% (Wiser and Bolinger, 2008). Traditionally wind integration costs are paid by the end-user,
but system operators have begun to recover the integration costs of wind energy from wind plants
directly. In 2009, Bonneville Power Authority (BPA) introduced a tariff of $5.7 per MWh for wind
plants within its system to recover the costs of integrating wind power (BPA, 2009). BPA was the
first system to charge wind generators for the integration costs of wind energy and other systems
are considered likely to follow suit (Kirby and Milligan, 2006).
Wind plant owners may implement solutions to mitigate variability if they are charged for
integration costs. A wind plant will be willing to pay up to the tariff imposed by the system for a
solution that completely eliminated the variability it produces. In BPA this would be $5.7 per MWh.
Realistically it is not cost effective to completely firm the power output of a wind plant. The costs of

42
integrating wind power are incurred mainly at hourly and subhourly time scales and wind power is
variable over time scales of subminute to weekly (Northwest Wind Integration Action Plan, 2007;
Katzenstein et al., 2010; Apt, 2007). Wind plants will seek to use flexible technologies to reduce
their variability in the hourly and subhourly time scales.
Here we develop a metric to determine the cost of variability of individual wind plants and
then show its use in valuing reductions in wind power variability. Keith and DeCarolis state that it
should be “possible…to assess the overall cost of wind’s intermittency” by “portioning the cost of
wind’s variability between various markets…and market participants” (Keith and DeCarolis, 2005).
Here we present an unbiased method to partition wind energy between hourly and subhourly
markets and use the corresponding market prices to determine the cost of variability from individual
wind plants.
The methods used to estimate the integration costs of bulk wind energy are not suitable to
evaluate reductions in wind power variability for individual wind plants. First, all of the integration
studies have focused on the net wind energy in a system and not the energy produced by individual
wind plants. Second, the integration studies use large complex models that are either proprietary or
difficult to replicate and are inappropriate to implement on a small scale. Third, the majority of the
studies have focused on future large penetrations of wind energy instead of current levels.
There are additional advantages to estimating the variability cost of individual wind plants
instead of the net wind power in a system. First, doing so provides a method to determine cost
effective solutions to reduce wind power variability. Second, it is important to determine if all wind
plants in a system equally contribute to the wind integration costs or if there are a few wind plants
sited in poor locations that are causing the majority of the incurred costs. Finally, system operators

43
may be able to prioritize wind plant projects in their interconnection queues to minimize their
integration costs for wind energy.
3.4 Data
We use 15-minute time sampled wind power data from 20 ERCOT wind plants in 2008 and
2009. In addition, we use 15-minute ERCOT balancing energy service (BES) price data and hourly
load following and regulation capacity price data for years 2004 through 2009. The locations of the
20 ERCOT wind plants are plotted in figure 3-7 in appendix B. Figures 3-8 through 3-13 in appendix
B are box plots of the ERCOT ancillary service prices for years 2004 through 2009.
3.5 Methods
Our method partitions all of a wind plant’s energy among the suite of markets available. We
first describe a generalized formulation of this principle that is representative of the electricity
markets in the United States and then present a metric specific to ERCOT. The three types of
services a generator in a United States electricity system can provide are energy, capacity, and
ancillary. Each service is necessary to maintain a functioning electricity system although each
electricity system in the United States does not offer competitive markets for all of the services
described.
Providing energy is the primary service of an electricity system, accounting for 70 to 95% of
the wholesale cost of electricity (ISO New England, 2009; PJM, 2009; Potomac Economics, 2009).
Energy markets are typically operated on an hourly basis and, depending on the ISO, a generator can
submit bids for each hourly interval in day-ahead markets, hour-ahead markets, or real time
markets. System operators accept enough generator bids to meet the predicted load for a given
hour plus a specified reserve margin. Generators whose bids are accepted are required to supply
power at the specified level for that hour.

44
From a system point of view, capacity markets ensure a system has enough generators it
can call upon to meet their maximum load plus a reserve margin. From a generator’s point of view,
energy markets are designed for generators to recover their variable costs while capacity markets
are designed for generators to recover their fixed costs. Capacity markets are typically longer term
markets that operate on a yearly basis.
Ancillary services are a suite of products designed to handle the variability present in an
electrical network. Variability exists in electricity grids due to fluctuations in load, transmission, and
generation. The nature of electrical networks and the lack of cost effective storage in electricity
systems means that the exact amount of electricity produced must be consumed if the system is to
remain stable. Small deviations can be tolerated but need to be corrected according to the
standards set by the North American Electricity Reliability Council (NERC). The suite of ancillary
services are traditionally defined as load following, regulation, energy imbalance, spinning reserve,
supplemental reserve, frequency control, voltage control, nonoperating reserve, and standby
service (Hirst and Kirby, 1997).
Renewable energy credit (REC) markets value the additional benefits renewable energy
generators add to a system. The primary benefits of renewable energy are that it is a zero emissions
source and that it satisfies policy goals mandated by over 29 states. The additional yet less tangible
benefits are a decreased dependence on foreign energy sources, an increase in portfolio diversity,
and a hedge against future fuel prices. Typically, one renewable energy credit is the environmental
and social value of one MWh of renewable energy.
From a system operator’s point of view, the value of energy from a wind plant is the sum of
the wind plant’s energy, capacity, REC, and ancillary service benefits and its ancillary service costs.
The costs of incorporating wind power into a system can be classified based on the two defining

45
characteristics of wind power: uncertainty and variability. Systems incur costs due to wind power’s
uncertainty because system operators can never know with a 100% certainty what the output of a
wind plant will be at a given time. The difference between the forecast and the actual output of a
given wind plant must be eliminated using either hourly energy markets or ancillary services
markets. We do not estimate the cost of forecast errors in this paper but note that the cost of
forecast errors can be included in our metric.
Wind power variability, the fact that the output of a wind plant is constantly changing, also
causes systems to incur costs. Any change in the power output of a wind plant must be
compensated by another source in the system. This source could be other wind plants, loads,
conventional generators, or energy storage. If conventional generators are used, the inefficiencies
suffered due to changing its power level are costs directly related to wind power. We note that
wind power variability also changes the loading of transmission lines and we do not attempt to
calculate the resulting changes in transmission profitability.
We estimate the cost of wind power variability in ERCOT by partitioning the power output of
a wind plant between hourly energy and ancillary service markets (figure 3-1). For each hour, we
determine a constant amount of a wind plant’s energy to partition to the hourly energy market. We
remove the hourly energy component from the wind signal and then determine the residual
ancillary services required. For the example in figure 3-1 we assume a simplified ancillary services
market, representative of ERCOT’s ancillary services, that consist of load following and regulation
markets. Regulation is the ancillary service that handles rapid fluctuations on time scales of minutes
and load following is the ancillary service that handles larger fluctuations on time scales of 15
minutes. We first determine the amount of load following capacity and energy needed and then
determine the amount of regulation capacity and energy required. We do not attempt to calculate

46
the capacity or REC benefits of wind plants because they do not affect the variability costs of wind
plants. Only the energy portioned to the hourly energy market affects the estimated variability cost.
Figure 3-1 - Conceptual diagram of how we partition wind energy into hourly energy, load
following, and regulation components.
Equation 3-1 is the simplified formulation of the variability cost of wind energy for wind
plants in ERCOT. We calculate only the load following component of the ancillary service cost of
wind energy because we were able to obtain only 15-minute time-resolved wind energy data for 20
ERCOT wind plants. The yearly variability cost of energy from a wind plant is the sum of its hourly
costs.
Load Following
Component
R
egulation
C
om
ponent
H
ourly
Energy
C
om
ponent
Wind Energy
0 15 30 45 60 min
t
Each hour decompose wind energy
into the following components
Up Energy
Down Energy
↓ Capacity
↑ Capacity
← qH
← qH

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